Aims. In the era of large sky surveys, photometric redshifts (photo-z) represent crucial information for galaxy evolution and cosmology studies. In this work, we propose a new machine learning (ML) tool called Galaxy morphoto-Z with neural Networks (GaZNet-1), which uses both images and multi-band photometry measurements to predict galaxy redshifts, with accuracy, precision and outlier fraction superior to standard methods based on photometry only. Methods. As a first application of this tool, we estimate photo-z for a sample of galaxies in the Kilo-Degree Survey (KiDS). GaZNet-1 is trained and tested on similar to 140 000 galaxies collected from KiDS Data Release 4 (DR4), for which spectroscopic redshifts are available from different surveys. This sample is dominated by bright (MAG_AUTO < 21) and low-redshift (z < 0.8) systems; however, we could use similar to 6500 galaxies in the range 0.8 < z < 3 to effectively extend the training to higher redshift. The inputs are the r-band galaxy images plus the nine-band magnitudes and colors from the combined catalogs of optical photometry from KiDS and near-infrared photometry from the VISTA Kilo-degree Infrared survey. Results. By combining the images and catalogs, GaZNet-1 can achieve extremely high precision in normalized median absolute deviation (NMAD = 0.014 for lower redshift and NMAD = 0.041 for higher redshift galaxies) and a low fraction of outliers (0.4% for lower and 1.27% for higher redshift galaxies). Compared to ML codes using only photometry as input, GaZNet-1 also shows a similar to 10%-35% improvement in precision at different redshifts and a similar to 45% reduction in the fraction of outliers. We finally discuss the finding that, by correctly separating galaxies from stars and active galactic nuclei, the overall photo-z outlier fraction of galaxies can be cut down to 0.3%.